Series Demystified 5

Algebra Level 5

\[ \large \sum_{n=1}^{46} \frac {(n^3-n^2-3n-4)}{(n-1)!} \]

If the summation above equals to \(S\), evaluate \( (46!S-1)^{\frac{1}{3}} \).

This is one of my original Series Demystified problems.
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