Seemingly Random Polynomial

Algebra Level 4

\[ \large x^{63} + x^{44} + x^{37} + x^{31} + x^{26} + x^9 + 6 \]

If \(x\) satisfies the equation \( \left(x + \dfrac1x\right)^2 = 3 \), then find the value of the expression above.

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