I am drunk-, fast- and dumb enough that it just might work!
Hanging hyphens are normally used to be parallel with a hyphenated compound (e.g. "ninetheenth- and twentieth-century writers"). There's no such hypenated compound after the conjunction and so this is very strange and hard to understand.
I am drunk, fast and dumb enough that it just might work!
This is fine. It's possible to interpret it part-way through as "I am drunk. Also I am fast. Also..." but it's not a horrible lurch on reading to readjust when it becomes clear it means "I am drunk enough…" etc.
I am drunk enough, fast enough and dumb enough that it just might work!
Much better. It means the same thing as the previous example but it's clearer in the meaning of each, and has a much better rhythm. It's not more correct than the other, but as well as being clearer in its use of the adverb enough, it's the rhythm of the lovely repetition I'd favour it for.
Aside: Repetition at the end of a clause or phrase, incidentally, is called epistrophe in the study of rhetorical techniques. Other uses of repetition include antanaclasis, epizeuxis, conduplicatio, anadiplosis, anaphora, mesodiplosis, diaphora, epanalepsis and diacope. That we have ten different names for different types of repetition is evidence in itself that repetition isn't necessarily a bad thing. Repetition tends only to be bad if it both adds nothing and repeats something relatively "heavy". Repetition of "light" units (like said tags on dialogue) tends not to even be noticed, and repetition that builds up a rhythm can be the best thing in a piece (it's the best thing in the sentence above). A danger for writers is that things can seem like dreadful repetition on writing or scanning that are unnoticeable or actually strong on actual reading.