Length of the intersection line

Find the length of the cloused intersection line of two surfaces

$\begin{cases} x^{2}+y^{2}+z^{2}=1 \\\\ x^{3}+y^{3}+z^{3}=\frac{1}{6} \end{cases}$

Give answer accurate to two decimal places. Calculate using computer.

Example for case $\begin{cases} x^{2}+y^{2}+z^{2}=1 \\\\ x+y+z=\frac{1}{6} \end{cases}$ see on picture

The task arose thanks to this problem