Evaluate the double series
$$
\sum_{j=0}^{\infty} \sum_{k=0}^{\infty} 2^{-3 k-j-(k+n)^{2}}
$$The answer is in the form \frac{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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