My source said that someone "was fooling around with Cardan's formula for solving x^3 + 6x = 20 and came up with (10 + sqrt(108))^(1/3) + (10 - sqrt(108))^(1/3) as a solution. Of course that has to equal 2, but the question is 'how do we know'? If we simply cube each of the radicals, we end up eventually with the original equation."

And my question is: Can you prove this?

(I have a simple proof which I'll post if no one does so first.)