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- Feb 14, 2012

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Find positive integers a and b such that:

$\displaystyle \left(\sqrt[3]{a}+\sqrt[3]{b}-1 \right)^2=49+20\sqrt[3]{6}$

This one appears to be tough because it doesn't seem right to expand the left hand side and I have tried that but it lead me to nowhere closer to finding both integers values for a and b.

Also, I've tried to work on the right hand side as my effort revolved around rewriting it as the square of sum of two terms but this has not been a fruitful approach as well.

Do you guys have any idea on how I can solve this one, please?

Thanks in advance.