4.51 Find the sum of all roots of the following equation
$$\sqrt[4]{x}=\frac{12}{7-\sqrt[4]{x}}$$
[Solution] Let $y=\sqrt[4]{x}$, then $y=\frac{12}{7-y}$, which gives $y^{2}-7 y+12=0$,
solving for
$$y_{1}=3, y_{2}=4$$
$$\text { hence } \quad x_{1}=3^{4}, x_{2}=4^{4} \text {. }$$

Therefore, the sum of all roots $x_{1}+x_{2}=3^{4}+4^{4}=337$.