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 \( a + b \).