Thermodynamic Processes question from JEE Main 2025 (3 Apr, Shift 1)

A piston of mass $M$ is hung from a massless spring whose restoring force law goes as $F = -kx^{3}$, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' $n$ ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $L_0$ to $L_1$, the total energy delivered by the filament is:(Assume spring to be in its natural length before heating)