  In this paper we aim at generalizing the results of A. K. Zvonkin and A. Y.
Veretennikov on the construction of unique strong solutions of stochastic
differential equations with singular drift vector field and additive noise in
the Euclidean space to the case of infinite-dimensional state spaces. The
regularizing driving noise in our equation is chosen to be a locally
non-H\"{o}lder continuous Hilbert space valued process of fractal nature, which
does not allow for the use of classical construction techniques for strong
solutions from PDE or semimartingale theory. Our approach, which does not
resort to the Yamada-Watanabe principle for the verification of pathwise
uniqueness of solutions, is based on Malliavin calculus.
