If the two system of equations

\(\begin{cases} ax+by=1\\ 3x-y=2\\ \end{cases}\)

\(\begin{cases} x+2y=1\\ ax-by=-2\\ \end{cases}\)

has the same solution \((x,y)\), then the value of \(a+b\) is \(\frac{m}{n}\) for relatively prime \(m\) and \(n\). Find \(m+n\).

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