  We report on radio and X-ray monitoring observations of the BHC Swift
J1753.5-0127 taken over a ~10 year period. Presented are daily radio
observations at 15 GHz with the AMI-LA and X-ray data from Swift XRT and BAT.
Also presented is a deep 2hr JVLA observation taken in an unusually
low-luminosity soft-state (with a low disk temperature). We show that although
the source has remained relatively radio-quiet compared to XRBs with a similar
X-ray luminosity in the hard-state, the power-law relationship scales as
$\zeta=0.96\pm0.06$ i.e. slightly closer to what has been considered for
radiatively inefficient accretion disks. We also place the most stringent limit
to date on the radio-jet quenching in an XRB soft-state, showing the connection
of the jet quenching to the X-ray power-law component; the radio flux in the
soft-state was found to be $<21~\mu$Jy, which is a quenching factor of
$\gtrsim25$
