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Suppose you have a well-shuffled standard deck of cards, (faces down). You start turning over the cards, one at a time, from the top of the deck. Let \(S\) be the expected number of cards you need to turn over before revealing all four \(7\)'s.

If \(S = \dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, then find \(a + b.\)

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