I have successfully used a battry-powered voltage testing screwdriver to find a blown bulb in a set of series connected Christmas tree lights. The LED will glow as the tip is moved from the live end of the loop until after the blown bulb at which point the LED turns off or glows much more dimly.
In my case the problem was simplified by the wiring being one large loop rather than a line with the return wire twisted alongside it.
As PlasmaHH says, "Why would you even want to?". You are going to have to joint the cable and it would be much safer to replace it. The break may have been caused by flexing in which case the adjacent region may all be week as may the neutral and - potentially more dangerous as there will be no external sign of failure - the earth.
If the internal conductors have broken there is a good chance that the insulation is damage or thinned out too. Don't touch the cable during testing. Put one hand in your pocket and with the other grip the tester up near the pocket clip while touching the metal button on the top with a finger or thumb. Trace the tip along the insulation. Unplug the cable when testing is complete.