Let $C$ be the class of all real valued continuously differentiable functions $f$ on the interval $0<x<1$ with $f(0)=0$ and $f(1)=1$. Determine the largest real number $u$ such that
$$
u \leqslant \int_{0}^{1}\left|f^{\prime}(x)-f(x)\right| d x$$
for all $f$ in $C$. The original answer is in \(\frac{m}{ne}\) format, please provide the value of m+ n.

Let's think step by step and output the final answer within \boxed{}.
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