Minimax!

Algebra Level 5

For \(S = \dfrac {\sqrt a - \sqrt b}{\sqrt {a - \sqrt b}}\), where \(a \ne b\) are real numbers, wthe range of \(S\) is \(k_1 \leq S \leq k_2\), where \(k_1 \) and \(k_2\) are real numbers. Evaluate \(k_1+k_2\).

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