Prove (√(3√3+19√7) - (4√2)(√√3))^(1/5) + ((3√2)(√√3))^(1/5) = (√(3√3+19√7) + (4√2)(√√3))^(1/5)

All right, these puzzles have been getting too easy for you guys. I'll crank this up a few notches now. Problem is getting the equations to fit in the question box.

Update:

Cool_joh, (4√2)(√√3) means

(4)(2^(1/2))(3^(1/4))

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