If maximum value of \( \int_{0}^{1}(f(x))^{3} d x \) under the condition \( -1 \leq f(x) \leq 1 ...

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If maximum value of \( \int_{0}^{1}(f(x))^{3} d x \) under the condition \( -1 \leq f(x) \leq 1 ; \int_{0}^{1} f(x) d x=0 \) is \( \frac{p}{q} \) (where \( p \) and \( q \) are relatively prime positive integers.). Find \( p+q \).
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