Gray tank won't drain

I had this about a month ago. I fulltime too and hadn't moved in a long time. Eventually enough stuff did get down the sink drain and built up enough and blocked the outlet above the shutoff valve. I guess just because it wasn't moving fast enough. As mentioned in an above post, I got a bucket and put it under the outlet and shoved a soft thin bendable stick up the outlet (drain snake would be the proper tool but I didn't want to go get one) and it unclogged the drain. A mess of nasty water and chunks that had the smell and look of vomit (sorry) came out before I could get the stick back out and the outlet valve closed again, but I caught most of it in the bucket. Hooked up the stinky slinky again and then drained the rest of the full grey tank.