You need to put water in the black tank before it is used so that the poop doesn't build up like that. Also add water to the bowl before will help.
Now for your current problem, you need to break it up some how. Some use a stick down the toilet, others just reach down there and squish it up with their hand. Afterwards you will need to rinse the tank out well. They make rinsers that connect to the outlet or go down the toilet. Just don't overfill the tank as you are rinsing it.
We have had a Amerilite for 3 seasons now and love it.