\[ \left( \sqrt [ 3 ]{ 1+a } -1 \right) { x }^{ 2 }+\left( \sqrt { 1+a } -1 \right) x+(\sqrt [ 6 ]{ 1+a } -1)=0 \]

Let \(\alpha \) and \(\beta \) be the roots of the equation (of \(x\)) above for \(a> - 1\).

Find the values of \( \displaystyle \lim_{a \to 0^+} \alpha \) and \( \displaystyle \lim_{a \to 0^+} \beta \) respectively.

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