Words can't end in "n" in Portuguese (Brazilian or otherwise), so the "n" is replaced with an "m" with very few exceptions like pólen (polen). It's worth noting that in Portuguese we don't pronounce the ending "m" or "n" for that matter. In other words, your lips don't touch at the end of "dindim". Both the "n" and the "m" in that word only serve to turn the short i into a nasal i. Try pronouncing the word "inn" without letting your tongue move at all and you'll get the idea, if you're not familiar with the sound.

"N"s also can't come before "P" or "B", in which case they also get replaced by "m". This is true in Spanish as well, though the first rule isn't.