Very complicated, isn't it?

Algebra Level 5

\[\large f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f\]

Function \(f(x)\) above, where \(a\), \(b\), \(c\), \(d\), \(e\) and \(f\) are rational numbers, is such that \({ (x - 1) }^{ 3 } | f(x) + 1\) and \({ (x + 1) }^{ 3 } | f(x) - 1\) and \(ace = \dfrac { p }{ q }\), where \(p\) and \(q\) are coprime integers. Find \(\sqrt { pq }\).

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