I am not sure... I think if I got 12' length 2 x 6 it might go edge to edge with a "joint" in the middle wall. I will have to get back up in the attic and measure my room walls. Appraisal documents show that I have 30' between front and rear exterior walls. So it may fit... I have bays and outcrops. If not including those than its 26'. So I would need to go out to the ceiling wall correct so some locations I would only need 26' of new beam and in other spots 30'. They don't make 15' or longer 2x 6 do they?
Edit: looks like they make 2x6 in lengths 8', 10', 12', 14', 16' and 20'... so should be able to span the whole room while having a "joint" in the middle.