Based of your question it appears that you have correctly assessed and identified the critical piece holding blacks position together. The Bishop on c6.
Rxc6 - Removing the Defender.
[FEN "4r1k1/1p3ppp/2b5/5n2/pp6/8/P4PPP/2R1R1K1 w - - 0 1"]
1. Rxc6 Rxe1#
Results in a completely lost position which allows black to mate in one.
Rxe8 - "...