The kitchen sink (both sides) are very slow to drain.

I took everythink apart under the sink and cleaned all the pipes, ran a snake through the lines from the sink, ran the snake from the outside towards the sink and all appears clean.

I put everything back together and the water would not drain. I turned on the garbage disposal and water came up the other sink. I thought the problem might be the air vent that goes through the roof. I ran the snake from the top of the air vent downward. A few feet down it felt like it was going through some type of a flipper. I passed the snake all the way down to about ground level.

The kitchen sink still will not drain.