Adopted from the Vermont Math contest

Algebra Level 3

Find the smallest positive real \(x\) such that \(\big\lfloor x^2 \big\rfloor-x\lfloor x \rfloor=6.\) If your answer is in the form \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, submit your answer as \(a+b.\)

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Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.