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Algebra Level 2

\[ \begin{eqnarray} f_1 (x)&=&x\\ f_2 (x)&=&1-x\\ f_3 (x)&=&\frac{1}{x}\\ f_4 (x)&=&\frac{1}{1-x}\\ f_5 (x)&=&\frac{x}{x-1}\\ f_6 (x)&=&\frac{x-1}{x}\\ \end{eqnarray} \]

If we know that \( f_6 (f_m(x))=f_4(x) \) and \( f_n (f_4(x))=f_3(x) \), find the minimum value of \(m+n\).

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