Is it a 5th degree Polynomial?

Algebra Level 4

\[\large \begin{align} a + 4b + 9c + 16d + 25e & = 1 \\ 4a + 9b + 16c + 25d + 36e & = 8 \\ 9a + 16b + 25c+ 36d + 49e & = 23 \end{align} \]

Real numbers \(a\), \(b\), \(c\), \(d\), and \(e\) satisfy the system of equations above. Find \(a + b + c+ d + e\).

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