How to unclog dual kitchen sink one side with a garbage disposal?

How to unclog dual kitchen sink one side with a garbage disposal?
Both drains in the kitchen sink are moving water very slowly. When garbage disposal is turned on the water keep coming back into the sink on both sides?
I opened the trap pipes on both sides and it was clear. I tried pouring hot water with baking soda but it does nothing. I bought drain snake and put into the pipe far passing the wall but it still does the same thing. Very slow drain.
Appreciate your input. Thank you.

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