Noise cancelling headphones are probably the wrong analogy here.

The better example is the differential signalling used in professional audio and many digital signaling protocols like Ethernet, HDMI and USB.

Instead of using one wire, referencing to ground, they send the signal as the difference between both wires. Both wires end up carrying the same signal with inverted polarity. Because both wires are running next to each-other any external noice will be applied to both equally.

The voltage will change, but the difference in voltage between both wires is untouched. And when you subtract the two voltages at the receiver end, any noise simply gets subtracted out.