Việt's polynomial

Algebra Level 5

Suppose that \( \alpha = \sqrt[7]{\frac{3}{5}} + \sqrt[7]{\frac{5}{3}} \) is a root of the 7th degree polynomial \(f(x)\) which has integer coefficients and a leading coefficient of \( - 15 \). What is the value of \( f(1)\)?

This problem is posed by Việt L.

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