The rational root theorem won't help

Algebra Level 4

x3+3x2+3x+5=0 \large x^3 + 3x^2 + 3x + 5=0

If the real value of xx that satisfies the above equation is in the form a+b3 -a + \sqrt[3]{-b} , where a a and b b are positive integers and b b is cube-free, find a+b a + b .

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