...one set for cleaner tones, the other set for dirtier tones, what would be the best way to accomplish this?

Using a regular amp splitter won't work, because those split the signal from the guitar and route it to two different paths...and with the 11R having one main in, I don't see that working.

Essentially, I guess what I am wanting to accomplish is to choose the path out of the 11R to either be separated to one of two amps, or to go to both at once (when chosen).

Thoughts?