sum of complex roots real ?

Question:sum of complex roots real ?

Posted: ThU 891 Product: Maple 17

July 24 2013

I have reason to believe that the expression below is a real number:

(1/6)*(-108+(12*I)*sqrt(1419))^(1/3)+10/(-108+(12*I)*sqrt(1419))^(1/3)+1;

A numerical approximation supports that. How can Maple help here to get a simplified expression?

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