The most extreme ultraluminous X-ray sources (ULXs), with $L_\mathrm{X} > 5 \times 10^{40}$ erg s$^{-1}$, are amongst the best candidates for hosting intermediate-mass black holes (IMBHs) in the haloes of galaxies. Jet radio emission is expected from a sub-Eddington accreting IMBH in the low/hard (radio bright) state. In a search for such IMBH jet radio emission, we have observed with the Very Large Array (VLA) at 5 GHz a sample of seven extreme ULXs whose X-ray properties indicate they are in the hard state. Assuming they remain in this state, the non-detection of radio emission for six of the target sources allows us to constrain their black hole mass to the IMBH regime, thus ruling out a supermassive black hole nature. For the extreme ULX in the galaxy NGC\,2276, we detect extended radio emission formed by two lobes of total flux density 1.43 $\pm$ 0.22 mJy and size $\sim$650 pc. The X-ray counterpart is located between the two lobes, suggesting the presence of a black hole with jet radio emission. The radio luminosity allows us to constrain the black hole mass of this source to the IMBH regime; hence, the extreme ULX in NGC\,2276 could be the first detection of extended jet radio emission from an IMBH. The radio emission could also possibly come from a radio nebula powered by the ULX with a minimum total energy of $5.9 \times 10^{52}$ erg, thus constituting the most powerful and largest ULX radio nebula ever observed.