Level of English depends heavily on where youre talking to people but generally in any city the size of Dresden you should be perfectly fine with just English.
Arsedoc mentioned it already though Dresden is a highly problematic city, there are scores of far right trash everywhere, it's permeated through the whole city not just bald hools in dodgy pubs. If you were French or British it probably wouldn't be an issue but since you're from SE Europe - that general area is one of the worst in terms of being targeted with venomous xenophobia.
Sorry to not be able to give you a warmer welcome. If you found a job in Frankfurt or Stuttgart not only would you be welcome nobody would even be able to tell whether you've been here five weeks or years, some expats depending on the line of work don't even bother learning German. As for Dresden (Eastern Germany in general, but Leipzig eg isn't nearly as bad): you genuinely couldn't pay me enough to go there. Its a nice little city but if you look anything like Frank Zappa you might run into trouble. If you don't or you're comfortable enough to deal with those situations, are certain you'll never run into the wrong part of town or God forbid the stadium then go for it.
