245 followers problem

Algebra Level 5

Given that \( x\) and \(y\) are positive reals satisfying \(\dfrac1x + \dfrac{245}y = 1\), the minimum value of \[x+y+ \sqrt{x^2+y^2} \] can be expressed as \( A+ B\sqrt C\), where \(A,B\) and \(C\) are positive integers with \(C\) square-free. Find the value of \(A+B+C\).

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