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Algebra Level 3
  • \(\sqrt[3]{a} + \sqrt[3]{b}\) is a root of \(10x^3 - 30x - 29\).
  • \(\sqrt[5]{a} + \sqrt[5]{b}\) is a root of \(10x^5 - 50x^3 + 50x - 29\).
  • \(\sqrt[7]{a} + \sqrt[7]{b}\) is a root of \(n_1x^7 + n_2x^5 + n_3x^3 + n_4x + n_5\).

If \(\gcd(n_1, n_2, n_3, n_4, n_5) = 1\) with \(n_1 > 0 \), what is the value of \(|n_1|+|n_2|+|n_3|+|n_4|+|n_5|?\)

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