For a particular peculiar pair of dice, the probabilities of rolling $1$, $2$, $3$, $4$, $5$ and $6$ on each die are in the ratio $1:2:3:4:5:6$. What is the probability of rolling a total of $7$ on the two dice? Provide your answer as a fraction in the form \(\frac{k}{m}\) and calculate the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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