Let \(m\) and \(n\) be positive integers satisfying \[n! + 76 = m^2. \]

If all the solutions of \((m,n) \) are \((m_1, n_1) , (m_2, n_2) , \ldots , (m_k , n_k ) \), submit your answer as \( \displaystyle \sum_{j=1}^k (m_j + n_j) \).

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**Notation:** \(!\) is the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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