Looks like there's more tree roots in there than Golden Cane roots. I have a lot of Golden Canes, some of them the height of a 2 storey building. But they never develop a root mass like that. Regardless, if you cut out those roots they will grow back in time, often a very short time.

There are some ferns that will spread around in situations like that and provide a very lush looking background. They don't have a deep root system so as long as they're well watered they won't be affected, whatever dense root mass might be below.

Based on the direction those roots are coming from and the size of your palm, I'd also agree that those roots are not coming from your palm. If your neighbor has some large trees that could be the actual source of the roots. I've seen people have no problem planting things close to Arecas so I don't think their root systems are extremely extensive, but even if they are coming from your Areca (which could be possible if the roots just didn't have anywhere else to go) there are some plants that will help make that part of your yard look awesome despite the roots.
I would definitely consider planting some bromeliads. You'll need a nice and light soil and some people even put pebbles to keep them in place since bromeliads generally grow on trees not on the ground. But there are some larger bromeliads that look great in the ground and can grow really well. The best part is their root systems are very small so they don't require a lot of space in the soil to grow huge. Those will add a lot of color underneath your palm when planted in a large mass. I would only plant very nice and vigorous plants there since those will be the ones that are able to compete with the Areca.

You can always resort to potted plants. The Bromeliads as a border plant could cover up the pots and you can get pots that look really nice which will add to the tropical look also. Mandevillas don't make great long term potted plants because of how ridiculously well they can grow in frost free climates, but they might be something you want to consider planting every year.

Croton have been some of the most reliable potted plants for me because they take a very long time to outgrow their pots. Mine have been in the same pots for years and they are still very happy and are growing bigger every year. They will add a lot of color and can help cover up that fence.

Agaves will eventually get huge and one of the best parts about them is they do very well in pots because they won't need water and they don't need a lot of nutrients. Some species get really big and will cover up that spot in just a few years. Others like agave desmettiana variegata won't need a huge pot because they are short, but robust, growers.

Good luck!
-Alex

You are absolutely correct. They are Golden Cane roots. They have an extensive root system but not that deep. Try planting crotons and bromeliads.

How can I remove golden cane stumps I have just cut the palms down to ground level I’ve heard pool granuals and pool salt mixed to a paste with water may be the answer ?

Pool granules (chlorine based) and pool salt will get rid of algae. Would kill but wouldn't get rid of Golden Cane stumps.In the process you'd be poisoning your soil. I recently cut a very tall clump of Golden Cane to ground level but am leaving it to mother nature to get rid of what's in the ground.