It takes time, but fill your tank and then add a a box of Rid-x, used for septic tanks. Rid-x is a yeast (an emzine) that's made to break down solids. The only problem is, it takes time to do it. So fill the tank and let it sit a week or so. The build up will begin to break down and then you'll be able to drain it out. You might have to repeat a few times to get it all out.
You can also use an emzine eater for keeping drain pipes clean. In this case, I don't think you want a full tank of water, but enough to make the build up wet. The emzines will eat and dissolve the solids. Once soft, the solids will flush out.
Bleach is OK for sanitizing, but you really want to flush it out and not sit. It will deteriorate your slide valves and rubber if left alone.