Too many bases

\[ { \left( 01 \right) }_{ 2 }+{ \left( 34 \right) }_{ 5 }+{ \left( 67 \right) }_{ 8 }\quad =\quad { \left( \overline { AB } \right) }_{ 9 } \]

What are the digits \(A\) and \(B\) that satisfy the above relation?

Details and Assumptions:

  • \( \left( 34 \right)_5 \) represents a number, say \(34\), in base \(5\)
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