Which is it - "didn't used to" or "didn't use to"?

CK, or other native speakers, do you consider this correct English? To me, this kind of writing is similar to the recent "should of" replacing "should have" - i.e. horribly wrong.

But then you look at real-world examples that are certainly not written by illiterate people, such as this title:
http://www.imdb.com/title/tt0810829/

For the ones who are as confused as I just was about the correctness of this phrase, see here:
http://tatoeba.org/deu/sentences/show/28339


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See discussion here: #8035253.

Summary:

Best:
"I never used to smoke."

Also correct:
"I didn't use to smoke."

Controversial (and in my view and that of the New Oxford American Dictionary, wrong):
"I didn't used to smoke."

If this sentence is going to be on List 907, which CK repeatedly presents as a set of proofread and trustworthy sentences, I think the "never used to" variant should be used.

Duplicates of this sentence have been deleted:
x #2949339