A Pre-RMO question! -30

Algebra Level 2

An Infinite Geometric Progression has a sum of 20052005. A new series is obtained by squaring the each term of the original series. The sum of the new series is 1010 times the sum of the original series.

If the common ratio of the original series is mn\dfrac{m}{n} where mZ,nZ,gcd(m,n)=1m\in\mathbb{Z},n\in\mathbb{Z},\gcd(m,n)=1, then find the sum of the digits of m+nm+n

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