3. Positive numbers $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}$ simultaneously satisfy
$$
\begin{array}{l}
\frac{x_{2} x_{3} x_{4} x_{5} x_{6}}{x_{1}}=1, \frac{x_{1} x_{3} x_{4} x_{5} x_{6}}{x_{2}}=2, \\
\frac{x_{1} x_{2} x_{4} \cdot x_{5} \cdot x_{6}}{x_{5}}=3, \frac{x_{1} \cdot x_{2} x_{3} x_{5} x_{6}}{x_{4}}=4, \\
\frac{x_{1} x_{2} x_{3} x_{4} x_{6}}{x_{5}}=6, \frac{x_{1} x_{2} x_{3} x_{4} x_{5}}{x_{6}}=9 .
\end{array}
$$

Then the value of $x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}$ is
3. $1+\sqrt{2}+\sqrt{3}+\frac{11 \sqrt{6}}{6}$