The answer is an integer?

Algebra Level 3

2+4223+24223\large \sqrt[3]{ 2 + \sqrt{4- 2\sqrt{2}}} + \sqrt[3]{ 2 - \sqrt{4- 2\sqrt{2}}}

If xx equals the expression above, then find the value of x332x+4 x^{3} - 3\sqrt{2}x + 4 .

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