Solve for y

Algebra Level 3

Given that \(y\) is a real number such that

\[1-\frac{y-\frac{3y+1}{5}}{3}=\frac{y}{2}-\frac{2y-\frac{10-6y}{7}}{2},\]

and \(y\) can be expressed in the form \(-\frac{a}{b}\), where \(a\) and \(b\) are coprime, positive integers, find the value of \(a+b\).

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