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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