  For a smooth cubic fourfold Y, we study the moduli space M of semistable
objects of Mukai vector $2\lambda_1+2\lambda_2$ in the Kuznetsov component of
Y. We show that with a certain choice of stability conditions, M admits a
symplectic resolution $\tilde M$, which is a smooth projective hyperk\"ahler
manifold, deformation equivalent to the 10-dimensional examples constructed by
O'Grady. As applications, we show that a birational model of $\tilde M$
provides a hyperk\"ahler compactification of the twisted family of intermediate
Jacobians associated to Y. This generalizes the previous result of Voisin
arXiv:1611.06679 in the very general case. We also prove that $\tilde M$ is the
MRC quotient of the main component of the Hilbert scheme of elliptic quintic
curves in Y, confirming a conjecture of Castravet.
