How to find a chord with length $1/11$ of the function $\sum_{n=1}^\infty\frac{\mu(n)}{n}x^n$, where $x\in[0,1]$ and $\mu(n)$ is the Möbius function?

Question

Let $\mu(n)$ the Möbius function, see if your need its definition from this MathWorld, and we consider the function $$f(x)=\sum_{n=1}^\infty\frac{\mu(n)}{n}x^n,\tag{1}$$ over real numbers $[0,1]$.

Question. I would like to know how to find (the prime number theorem and the universal chord theorem, see if you need it this Wikipedia, imply the existence) a chord of length $\frac{1}{11}$ for our function $(1)$. Many thanks.

I don't know if it is obvious how to find it (I know how are the graphs of functions $\sum_{n=1}^N\frac{\mu(n)}{n}x^n$, over the same interval, for a large and fixed integer $N$), or well if it is very difficult and thus we only can to find an interval containing our chord.

References:

[1] Ralph P. Boas, A Primer of Real Functions, Mathematical Association of America 4th Edition (1996).