My kitchen sink(s) are back up and clogged. What can I do? I live in a single-family home beside a dual-basin kitchen sink. ...

I live in a single-family home beside a dual-basin kitchen sink. The right-side of the sink has a litter disposal, which is older, but surrounded by good working condition. When I use the disposal, marine backs up into the other side of the sink and consequently does not drain. When I plunge the left side of the sink, the river comes out the right side drain. I plugged the disposal side and plunged the other side, but this has not freed the clog. I hold tried drain-o, but that did not work. I own a 20 ft. snake, but I haven't tried that yet. I required to get some suggestion first!

Any advice would be greatly appreciated.
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Answers:    that exact entity is happening to my sink and the plumber said something give or take a few the pipes or what ever outside are not slanted right or something like that. I dont own I rent and the owners dont want to address the concern
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This happened to me going on for a month ago and I had to telephone a plumber to snake it. I tried everything that you did too but to no avail.