Max and min

Algebra Level pending

Given that \(-1 \leq x_i \leq 2\) for \(i=1, 2,..., n\) such that \( \displaystyle \sum_{m=1}^n x_m = 19 \) and \( \displaystyle \sum_{m=1}^n x_m ^2 = 99 ,\) find the ratio of the maximum and minimum values of \( \displaystyle \sum_{m=1}^n x_m ^3 \).

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