I take it that you mean a 5/16x24 NUT won't fit. Could it be a matter of cleaning the nut's threads with a 5/16x24 tap?

A rod and a bolt is the same, [outside thread]...Randy is correct, you mean a NUT, I could have another guess that the die used was a cheap oversize piece of Chinese chunk.

Not a Chinese tap and die set Konrad. But thanks for the input. For more information, I am trying to put more threads on an axle for a skateboard truck. I have noticed that the axle is slightly larger than that original 5/16 threads. I was able to add more threads but the newly threaded area still seems wider than the nut. I have also tried tap on the nut with no effect.

A good die is split on one side for adjustment with screw in the die holder.

I would assume you don't have this stile, yours in not split, [cheaper stile] even so, it should make a correct thread. Some pictures would help.