An algebra problem by Sheikh Sakib Ishrak Shoumo

Algebra Level 3

Let the zeros of \(7x^2+x+7=0\) be \(\alpha\) and \(\beta\). Now, \(\alpha^3 + \beta ^3 =\dfrac pq\) for some positive coprime integers \(p\) and \(q\). Find \(p+q\).

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