# 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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