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Number Theory Level 4

Given $a$ and $b$ are two integers that satisfy

$\large \text{lcm} \left(x^2 + ax - 2, x^2 + 5x + b\right) = x^3 + 4x^2 + x - 6$

Calculate $a + b$ .

Notation: $\text{lcm}(\cdots)$ denotes the lowest common multiple.

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