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 $zeta=0.96pm0.06$ 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 $gtrsim25$
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