$6.280 \sqrt{x}-\sqrt{x+1}-\sqrt{x+4}+\sqrt{x+9}=0$.

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$6.280 \sqrt{x}-\sqrt{x+1}-\sqrt{x+4}+\sqrt{x+9}=0$.
Solution. $\sqrt{x}+\sqrt{x+9}=\sqrt{x+1}+\sqrt{x+4} \Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{l}x \geq 0, \\ x+x+9+2 \sqrt{x(x+9)}=x+1+x+4+2 \sqrt{(x+1)(x+4)}\end{array} \Leftrightarrow\right.$
$\Leftrightarrow\left\{\begin{array}{l}x \geq 0, \\ 2+\sqrt{x(x+9)}=\sqrt{(x+1)(x+4)}\end{array} \Leftrightarrow\left\{\begin{array}{l}x \geq 0 \\ 4+x^{2}+9 x+4 \sqrt{x(x+9)}=x^{2}+5 x+4\end{array} \Leftrightarrow\right.\right.$ $\Leftrightarrow\left\{\begin{array}{l}x \geq 0, \\ x+\sqrt{x(x+9)}=0\end{array} \Leftrightarrow x=0\right.$.

Answer: $x=0$.

## $6.281 \sqrt[3]{x+5}+\sqrt[3]{x+6}=\sqrt[3]{2 x+11}$

Solution. Raise both sides to the third power:

$2 x+11+3 \sqrt[3]{(x+5)(x+6)} \cdot(\sqrt[3]{x+5}+\sqrt[3]{x+6})=2 x+11 \Leftrightarrow$

$\sqrt[3]{(x+5)(x+6)} \cdot(\sqrt[3]{x+5}+\sqrt[3]{x+6})=0 \Leftrightarrow \sqrt[3]{(x+5)(x+6)(2 x+11)}=0 \Rightarrow\left[\begin{array}{l}x=-5, \\ x=-6, \\ x=-\frac{11}{2} .\end{array}\right.$

By checking, we confirm that all these values are roots of the original equation.

Answer: $x_{1}=-6 ; x_{2}=-5.5 ; x_{3}=-5$.