. Now use L'Hopital.
The problem with that is that the limit you get is 1, when the actual limit is -1. So you should first consider which has the indeterminant form . Using l'Hopitals rule is an obvious thing to do.
The problem is, Wolfram Alpha is calculating the limit in the complex plane with the definition I first gave, but by what I understood the limit that was asked ignores this and uses only the fact negative numbers have odd roots (ie. we want the limit of a sequence, not the limit of the function)