I may sound crazy but connecting 2 ballasts in series should work, right?

According to Google, a ballast is an inductor, and connecting 2 inductors in series should just double it.

So can I use 2x 11w ballasts and create a 22w ballast?

The ballasts are the same brand and model.

Connect them in parallel, not series. And it only works with simple choke ballasts.

In fact, things are more complex, as inductors/coils/chokes, whatever they called, are not measured in watts, but in Ohms and Henries. In practice this means that circuit current depends also on lamp voltage, the fraction of line voltage that drops across the choke. I always advocate to use some adequate measuring tools not to experiment blindly.

When lamps have almost equal burning voltage, like most common T8-T12 fluorescent tubes in 120-150cm length, which all run at about 100-110V, yes you can roughly sum the ballast choke wattages and run them parallel.

Actually, it is possible to run more complex ballasts like leakage transformers (non-resonant) in parallel, and I can prove this too. The current just multiplies.

Yeah, I was being a little over-simplistic. I've never tried it with leak transformers, though