Just another die game

Ari and Brian play a sequence of independent games. Ari throws a die first and wins on a "six." If he fails, Brian throws and wins on a "five" or "six." If he fails, Ari throws and wins on a "four," "five," or "six." And so on. The probability of Ari winning the sequence is $$\color{blue}{\dfrac{a}{b}}$$, where $$\large\color{blue}{a}$$ and $$\large\color{blue}{b}$$ are positive coprime integers. Calculate $$\large\color{blue}{a+b}$$.

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