Near Mid-Air collision on Ryanair 6305 Barcelona to Bergamo?

I was on Ryanair flight 6305 on 21st october 2014 and while cruising, everything calm and hostesses serving drinks, pilots made a strong turn left climbing and accelerating hard. Just a moment later I saw a shadow passing in my window and when I turned to it there was the white contrail of another plane very closed to us with a completely different inclination, since we where still climbing. I did not see the plane, while another passenger behind me could do it, even if none of us was sure about the distance. The hostesses seemed not to realize what happened and I asked one of them who said she did not see anything but that she would ask the captain. She came back from the cockpit with the answer of the captain that said that indeed he moved away from an other airplane, American Airlines, but that everything was under control. Sure ! What would he say !
I checked the flight tracking and found this: … E/tracklog
Around 11.35 there is this steep turn and climb, exactly in that moment (I sent a what’s up to friends around 10.40, shortly after it happened).
I am not an expert and I am wondering how dangerous could have this been.

Bye !!