Compute
\[\sum_{j = 0}^\infty \sum_{k = 0}^\infty 2^{-3k - j - (k + j)^2}.\]The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

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