Can you guess what I guessed!

Algebra Level 5

x422x212x+22=0x^{4}-22x^{2}-12x+22=0 The above equation has roots of the form ±a±b±c\pm \sqrt{a} \pm \sqrt{b \pm \sqrt{c}}, where a,ba, b and cc are constant positive integers, and aa and b3\sqrt[3]{b} are relatively prime.

Find a+b+ca+b+c.

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