Yes, it is correct.
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AnonymousBoth the students and the teachers don't like the food.Universal quantifiers like both and all in the subject position don't work well when the predicate contains negation. You can get away with this, but I think there is a better way to do it.
AnonymousBoth the students and the teachers don't like the food.It's okay, but it would be better to switch to a positive sentence if you wish to use "both."