6.065. $\sqrt{2 x+5}+\sqrt{5 x+6}=\sqrt{12 x+25}$.
Solution.

Domain of definition: $\left\{\begin{array}{l}2 x+5 \geq 0, \\ 5 x+6 \geq 0, \\ 12 x+25 \geq 0\end{array} \Leftrightarrow x \geq-\frac{6}{5}\right.$.

By squaring both sides of the equation, we have

$$
\begin{aligned}
& 2 x+5+2 \sqrt{(2 x+5)(5 x+6)}+5 x+6=12 x+25 \Leftrightarrow \\
& \Leftrightarrow 2 \sqrt{(2 x+5)(5 x+6)}=5 x+14 \Rightarrow \\
& \Rightarrow 4(2 x+5)(5 x+6)=25 x^{2}+140 x+196 \Leftrightarrow 15 x^{2}+8 x-76=0
\end{aligned}
$$

from which $x_{1}=-\frac{38}{15}, x_{2}=2 ; x_{1}=-\frac{38}{15}$ does not satisfy the domain of definition. By checking, we confirm that $x=2$ is a root of the equation.

Answer: $x=2$.