Mirrored Cryptogram

Logic Level 2

\[\large \begin{matrix} & A & B & C \\ & B & B & C \\ + & C & C & C \\ \hline \\ \ \\ \ \end{matrix} \qquad \quad \begin{matrix} & C & B & A \\ & C & B & B \\ + & C & C & C \\ \hline \\ \ \\ \ \end{matrix} \]

\(A\), \(B\), and \(C\) in the two cryptograms above are distinct digits from 1 to 9. If the two cryptograms sum up to the same number, what is the smallest possible sum of each?

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