Power Play

The smallest number \(n\) greater than 1 such that \(\large \sqrt{n}\), \(\large \sqrt[3]{n}\), \(\large \sqrt[4]{n}\), \( \large \sqrt[5]{n}\), \( \large \sqrt[6]{n}\), \( \large \sqrt[7]{n}\), \( \large \sqrt[8]{n}\), \( \large \sqrt[9]{n}\), \( \large \sqrt[10]{n}\) are all integers can be expressed in the form \(a^{b}\), where \(a\) and \(b\) are both positive integers and with \(a\) as small as possible.

Find \(a+b\).

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