Columnar Addition?

\[ \large{\begin{array}{cccccccc} &0 .& 1 & 2& 3 & 1&2& 3 & 1&\ldots\\ +&0. & 0 & 1& 2 & 3&1& 2 & 3&\ldots\\ \hline &0. &1 &3 &5& 4 & 3&5&4&\ldots\\ \hline \end{array}} \]

The above shows the sum of the two fractions \( \dfrac{123}{999} \) and \( \dfrac{123}{9990} \) when written in decimal representation.

If \( \dfrac{123}{999} + \dfrac{123}{9990} = \dfrac1{10} + \dfrac{354}x \), find the value of \(x\).

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