One fair die has faces \(1, 1, 2, 2, 3, 3\) and another has faces \(4, 4, 5, 5, 6, 6\). The dice are rolled and the numbers on the top faces are added. Find the probability that the sum will be odd. The original answer is in \(\frac{k}{m}\) format, please give the value of k + m.

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