# Experimental... again

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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