Consecutive Products And Modulos!

Let \( S \) be the set of all natural numbers \( k \) such that \( k(k+1) \equiv 60 \pmod{72} \) and let \( S_{72} \) be the set of all elements of \( S \) modulo 72 (so, if \( k \in S \), then \( a \in S_{72} \) iff \(a < 72 \) and \( k \equiv a \pmod{72} \)). Find the sum of all elements of \( S_{72} \).

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