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$\begin{aligned} \begin{cases} x^2 + 3x - 7 &\equiv 0 \pmod{71} \\ x^2 - 5x - 16 &\equiv 0 \pmod{89} \end{cases} \end{aligned}$

Let $x$ be a positive integer satisfying the system of equations above. What is the least possible value of $x?$

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