Something's not right...
When attempting to clear the blockage, the drain pipe broke which is a sign of improper initial installation or a long term problem.
Soap, hair, dirt, and anything else going down your drain can accumulate and cause back ups.
Unfortunately the clog couldn't be removed from the drain and Bryan will have to cut out a portion of the kitchen ceiling to remove it. Don't wait for a back up! Get your drains cleaned when they start to slow down instead!