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Algebra Level 5

\[ \begin{cases} a^3 + 12ab+ 64=b^3 \\ a^4 + 256=b^4 \end{cases} \]

If \((a_1,b_1),(a_2,b_2) ,\ldots , (a_n,b_n) \) are real numbers which satisfy the system of equations above, find the value of

\[\displaystyle 1 + 27 \sum_{j=1}^n (b_j^3 - a_j^3). \]

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