It's tricky but personally if you really think this would be your only visit (I know many sensibly say don't plan on that basis, but it is hard to avoid doing so), I would include one southern city as a nice contrast to the other two cities. Otherwise I'd do just Madrid and Barcelona with some day trips - saving Sevilla for a second visit focusing on Andalucia.
One option would be 4 nights in Barcelona (no day trips needed, but you might like Girona as a smaller city for a day). Then fly to Sevilla and stay 3 nights. Currently, there is a flight at around 7am, so if you were willing to get up early you would have most of that day in Sevilla plus the whole of the next two. That might then be enough time to include a half day trip to Cordoba to see the mezquita/catedral (there's much more to Cordoba but that's undoubtedly the "must see" in the city and province). Then take the high speed train from Sevilla to Madrid and stay 3 nights. Depending on your interest in Madrid you might consider leaving the capital and day tripping to Toledo. Views on Madrid's attractions vary - are you interested in art galleries and large, but dull royal palaces?
I've assumed 11 days in total means 10 nights. The above is a fast pace (faster than we usually manage), but is doable and not, I think, unfeasibly rushed. But what is your tourism style? How quickly do you like moving?