# The rational root theorem won't help

Algebra Level 4

$\large x^3 + 3x^2 + 3x + 5=0$

If the real value of $x$ that satisfies the above equation is in the form $-a + \sqrt[3]{-b}$, where $a$ and $b$ are positive integers and $b$ is cube-free, find $a + b$.

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