  We consider stochastic differential equation $$ d X_t=b(X_t) dt +d W_t^H, $$
where the drift $b$ is either a measure or an integrable function, and $W^H$ is
a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1)$,
$d\in\mathbb{N}$. For the case where $b\in L_p(\mathbb{R}^d)$, $p\in[1,\infty]$
we show weak existence of solutions to this equation under the condition $$
\frac{d}p<\frac1H-1, $$ which is an extension of the Krylov-R\"ockner condition
(2005) to the fractional case. We construct a counter-example showing
optimality of this condition. If $b$ is a Radon measure, particularly the delta
measure, we prove weak existence of solutions to this equation under the
optimal condition $H<\frac1{d+1}$. We also show strong well-posedness of
solutions to this equation under certain conditions. To establish these
results, we utilize the stochastic sewing technique and develop a new version
of the stochastic sewing lemma.
