食堂の食べ物はあまり好きじゃないだ。 is not grammatical. じゃない cannot be followed by だ in standard Japanese, so the correct version of this sentence with the ん removed would simply be
As for the meaning, this is a straightforward ordinary usage of the "explanatory の", so it simply adds a certain explanatory nuance to the statement. A similar effect could be achieved in English by adding something like "you know" or "you see" to the end of the sentence, but it doesn't always need translating at all, since it's quite a subtle difference.
In a sense, I might actually consider the version of the sentence with the explanatory の to be more neutral than the version without it, since
食堂の食べ物はあまり好きじゃない。 sounds like a rather blunt statement that you'd be unlikely to use as-is in conversation, whereas
食堂の食べ物はあまり好きじゃないんだ。 sounds a little softened and so more like something you'd be likely to actually hear in a variety of contexts.