Neither One nor Two but Three Geometric Series in One

Level pending

Let \( \frac{1}{7} \) + \( \frac{3}{7^2} \) + \( \frac{6}{7^3} \) + \( \frac{10}{7^4} \) + \( \frac{15}{7^5} \) + \( ... \) = \( \frac{a}{b} \) , with \( a \) and \( b \) are coprime, what is \( a + b \) ?

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