We Need To Go Deeper - 5

\[\large \underbrace{(\ldots((((x!)!)!)! \ldots)!}_{\text{Infinitely many factorials}} =x \]

Find the sum of all integer solution(s) that satisfy the equation above.

Notation:

\(!\) denotes the factorial notation. For example, \(10! = 1\times2\times3\times\cdots\times10 \).

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