Escape velocity of an elephant form surface of planet is same as that escape velocity of a mouse. Is it TRUE?

The escape velocity of an object from the surface of a planet is given as:
$$\begin{gathered} v_e=\sqrt{\frac{2GM}{R}} \\ \text{where,} G\text{ is the gravitational constant} \\ M\text{ is the mass of the planet} \\ R \text{is the radius of the planet}. \end{gathered}$$
You can see that the escape velocity of an object from the surface of the earth is independent of the mass of the object. Therefore, the escape velocity of an elephant will be same as that of a mouse from the surface of a planet.