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\(p\) and \(q\) are real numbers where

\(p=\sqrt{\frac{17}{2}+6\sqrt{2}}+\sqrt{\frac{17}{2}-6\sqrt{2}}\)

and

\(q=\sqrt{\frac{17}{2}+6\sqrt{2}}-\sqrt{\frac{17}{2}-6\sqrt{2}}\).

Then \(\sqrt{2} (pq)^{-1}\) can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime integers.

What is the value of \(a+b\)?

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