A Pre-RMO question! -20

Algebra Level 3

Suppose that 4x1=5, 5x2=6, 6x3=7...126x123=127, 127x124=1284^{x_1}=5,\space5^{x_2}=6,\space6^{x_3}=7...126^{x_{123}}=127,\space127^{x_{124}}=128. If the product x1x2x3...x123x124x_1x_2x_3...x_{123}x_{124} is of the form mn, gcd(m,n)=1, mZ+, nZ+\frac{m}{n},\space\gcd(m,n)=1,\space m\in \mathbb Z^+,\space n\in \mathbb Z^+, find m+nm+n.

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