If \((2^x - 4^x) + (2^{-x} - 4^{-x}) = 3\), find the numerical value of the expression 
\[
(8^x + 3\cdot 2^x) + (8^{-x} + 3\cdot 2^{-x}).
\]

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