No

No I just put a queen in an 11x11 for guests and there is just enough room to walk around it

Pretty sure there should be, actually.

There may be room for it but check doors that swing in. My 11x13' bedroom can hold the width of an Eastern king with a meager 22" on either side of the bed but not a California king because the entry door would hit the corner of the longer bed. With only 2' on either side an off center bed isn't reasonable. I am fine with the aisle between dressers and queen bed in the 11x13' room but there would only be 17" even with the shorter Eastern king if you have dressers in a 11x11' room.

I wouldn't put an eastern king in my room though, the door would be grazing the bed's corner.