\(\sqrt[3]{{\displaystyle\frac{{{x^9} + 9{x^2} - 1}}{3}}} = 2x + 1\)

\(x_1,x_2,...,x_n \in \mathbb {R}\) are the solutions of this equation.

Let:

\(\displaystyle\frac{1}{\pi }\sum\limits_{i = 1}^n {\arccos \displaystyle\frac{{{x_i}}}{2}} = \displaystyle\frac{a}{b}\)

If \(a,b \in \mathbb {Z}, \gcd (a,b) = 1\), find \(a+b\)

Hint: Some calculus needs to be applied.

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