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, $10! = 1\times2\times3\times\cdots\times10$ .