The first sentence is incorrect and the second is also dubious.. I'm afraid it's a slightly a long story. This is informal: I'm afraid it's a bit of a long story.
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MustAskI've seen this in a dictionary "I'm afraid it's rather a long story." , where rather means "relatively" or "somewhat". That's the reason why I asked if "slightly" can be used in with the same sentence structure.It can be substituted as an adverb, where the adverb is a modifier of the adjective. eg.