It's definitely nasalized at the end 'tham' not 'tha' which tells you an article is there, but aye, in practice this is "tha'm brot blasta" just as anything with "tha thu" in it sounds like 'how' typically.
Put in the correct answer 'tha am brot blasta', said I was wrong and gave Tha brot blasta as the answer. I put that in and it said that was wrong and the first answer was correct. I had to try several times before my first answer was accepted. Confused