  We study the Gibbons-Tsarev equation $z_{yy} + z_x z_{xy} - z_y z_{xx} + 1 =
0$ and, using the known Lax pair, we construct infinite series of conservation
laws and the algebra of nonlocal symmetries in the covering associated with
these conservation laws. We prove that the algebra is isomorphic to the Witt
algebra. Finally, we show that the constructed symmetries are unique in the
class of polynomial ones.
