Disposal is working but water is backed up and won't go down.

Disposal is working but water is backed up and won't go down.
If both sides of the sink are blocked then you have a blockage in the laterial (horizontal) drain line in the wall. The solution would be to remove the "J" bend from the trap and send a snake up the tail of the trap into the wall.
You will hit a elbo about 8 inches in but once past that you only have to put out about 6 feet more. Flush out the line with hot water. Good luck, Tom