# 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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