2026 AIME II Problem 11

Find the greatest integer n such that the cubic polynomialx^{3} -\frac{n}{6}x^{2} + (n - 11)x - 400has roots \alpha^{2}, \beta^{2}, and \gamma^{2}, where \alpha, \beta, and \gamma are complex numbers, and there are exactly seven different possible values for \alpha + \beta + \gamma.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.