Vieta's is ok

Algebra Level 3

If \(a_1, a_2, \ldots, a_6\) denotes the roots of the polynomial \({ x }^{ 6 }+{ 4x }^{ 5 }+{ 43x }^{ 4 }+{ 3x }^{ 2 }-x+1\), compute \( \displaystyle \sum_{n=1}^6 \dfrac1{a_n} \).

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