The answer is an integer?

Algebra Level 3

\[\large \sqrt[3]{ 2 + \sqrt{4- 2\sqrt{2}}} + \sqrt[3]{ 2 - \sqrt{4- 2\sqrt{2}}} \]

If \(x\) equals the expression above, then find the value of \( x^{3} - 3\sqrt{2}x + 4 \).