Question: Convert an Expression

How do I convert the expression

y = (sqrt(x) + 10)^(1/3) - (sqrt(x) - 10)^(1/3);


y^3 = 20 - 3*(x - 100)^(2/3);

A post on the Maxima mailing list said this was done by cubing both sides.  I can not seem to be able to get there.  A suggestion that the process involved recognizing the product (a+b)*(a-b)

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