Sounds like oscillation because the FET is too much of a capacitive load on the opamp. Judging from the datasheets, your FET has only twice the input capacitance of the one used in Dave's video (500pF vs 1nF), but it can make a difference. Add a series resistance, say 1k, between the output of the opamp and the moset gate. Then add another resistor, also 1k, between the inverting input of the opamp and the source of the mosfet. Then add a capacitor, something like 1nF to 10nF from the output of the opamp to it's inverting input. Also ensure you have some decoupling across the power rails of the opamp and the potentiometer wiper, something like 100nF or 1uF.
That should eliminate any oscillation problems. I built a similar circuit and this is what I had to resort to in order to keep the circuit stable.