Newton's Sum Reversed

Algebra Level 5

If \(a,b,c,d \in \mathbb{R}\) such that

\[\begin{align} a^{7}+b^{7}+c^{7}+d^{7}&=2188\\ a^{6}+b^{6}+c^{6}+d^{6}&=858\\ a^{5}+b^{5}+c^{5}+d^{5}&=244\\ a^{4}+b^{4}+c^{4}+d^{4}&=114. \end{align}\]

Find \(a+b+c+d\)

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