I plunged the side without the disposal and both sides of water went down but when you try to run water, it immediately backs up again. I checked the p trap and it was clear. I then bought a hand crank snake and it reaches a certain point and will go no further (did this on both the disposal side and the other side). Tried serveral times to push past the blockage but it wouldn't go. Before I call a plumber, is there anything else anyone can suggest. (the house is on a slab so no basement access)
A plumber's snake will usually only plunge right through the grease and other organic kitchen gunk blockage.
Before calling a plumber, do what I do....use a good enzyme-based drain cleaner like DrainCare. You run warm water down the drains, pour in the DrainCare and let it eat the organic gunk out overnight, and then flush it all down with hot water. I always start the flushing the next morning with a kettle of boiling water. If the clog is really bad, you may have to do it more than once, but it always works.
Enzyme-based drain cleaners, unlike caustic drain cleaners, will not harm your fixtures or pipes or you.
Works for me!