No one was able to solve this problem when i posted it last time!

Find the smallest integer \(n\) such that (for some number of 1's)

\[ 999999 \times n = 111 \ldots 111. \]

It can be expressed as

\[ \frac{ 10 ^ {54} -1 } { b ( 10 ^ 6 - 1 ) }. \]

Find \( 10 + b \).

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