I recently renovated my master bathroom which included 2 new basins, shower, toilet and bathtub. The toilet and bathtub work fine. When using either basin the water comes out of the shower drainpipe. When using the shower the water backs up the recedes very slowly. The Installer used 20 feet of snake to try and fix the problem unfortunately it didn't work. Any suggestions. I am now looking for a professonal plumber who specializes in drain pipe problems. Any and all suggestions would be appreciated

The Installer used 20 feet of snake to try and fix the problem
Where did the installer snake from?
What size snake did he use? I would have first went down the shower drain and if that didn't get it I would have gone down the lavatory roof vent. Has this been done? Let me know, Tom