Freaky Factorials

\[\large n!(n-1)!=m!\]

Solve the equation above for natural numbers \(m,n\).

Let \(S = \{ (m_1, n_1), (m_2, n_2), \ldots, (m_j, n_j) \} \) denote all the possible solutions.

Evaluate \( \displaystyle \sum_{k=1}^j (m_k + n_k) \).

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