The English correct solution is wrong - it should read 'No, i didn't use [not used] to like coffee
My translation is correct - the English translation given is wrong i.e. it should read 'didn't use to like coffee' not 'didn't used to like coffee'
"The negative of used to is most commonly didn’t use(d) to. Sometimes we write it with a final -d, sometimes not. Both forms are common": http://dictionary.cambridge.org/us/grammar/british-grammar/used-to
See also http://languagelog.ldc.upenn.edu/nll/?p=2756 .
We can't see what "your translation" was -- presumably "...didn't use to like coffee"? That should be accepted. But I wouldn't say that "didn't used to like coffee" is wrong.
"used to" acts rather anomalously, as the LanguageLog entry makes clear.
I think more usual English might be "I used not to like coffee" (Ro'n i'n arfer yn hoffi ddim coffi (?)) although this is somewhat more affirmative than negative and the correct form of 'no' in Welsh would presumably depend upon the context or a preceding question? Also it tends to suggest a follow-up such as 'but I do now'.