  We theoretically study a strongly-driven optomechanical system which consists
of a passive optical cavity and an active mechanical resonator. When the
optomechanical coupling strength is varied, phase transitions, which are
similar those observed in $\mathcal{PT}$-symmetric systems, are observed. We
show that the optical transmission can be controlled by changing the gain of
the mechanical resonator and loss of the optical cavity mode. Especially, we
find that: (i) for balanced gain and loss, optical amplification and absorption
can be tuned by changing the optomechanical coupling strength through a control
field; (ii) for unbalanced gain and loss, even with a tiny mechanical gain,
both optomechanically-induced transparency and anomalous dispersion can be
observed around a critical point, which exhibits an ultra-long group delay. The
time delay $\tau$ can be optimized by regulating the optomechanical coupling
strength through the control field and improved up to several orders of
magnitude ($\tau\sim2$ $\mathrm{ms}$) compared to that of conventional
optomechanical systems ($\tau\sim1$ $\mu\mathrm{s}$). The presence of
mechanical gain makes the group delay more robust to environmental
perturbations. Our proposal provides a powerful platform to control light
transport using a $\mathcal{PT}$-symmetric-like optomechanical system.
