\( \triangle PQR \) is isosceles and right-angled at \( R \). Point \( A \) is inside \( \triangle PQR \), such that \( PA = 11 \), \( QA = 7 \), and \( RA = 6 \). Legs \( \overline{PR} \) and \( \overline{QR} \) have length \( s = \sqrt{a+b\sqrt{2}} \), where \( a \) and \( b \) are positive integers. What is \( a+b \)?

Let's think step by step and output the final answer within \boxed{}.
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