How much trouble is this worth to you...
Here's a very robust (I think... never tried it... but based on other stuff about long wire monitoring) "answer" for you:
With a different switch at the other end, at the "sense it" end, you could arrange for the voltages on the end of the wire NEAR... not directly connected to!!... the Arduino, call them "A" and "B", to be powered "one way" or "the other", depending on switch position.
Switch "on": A is positive with respect to B
Switch "off": B is positive with respect to A
Once that is in place, near the Arduino, you wire up a comparator circuit with a digital output to the Arduino.
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Less involved thing to try:
At Arduino, a small circuit based around an opto-isolator...
... and drive the LED in that with a larger voltage than the voltage you are currently using. (Larger voltage= more room for "must be higher than".)
The same circuit could incorporate a capacitor/ resistor on the LED side to discard transients.