"Both a line signal and a mic signal are prone to the same amount of noise from external sources using the same cable, you just would notice it much more on a mic signal."
You amplify noise along with the signal. Start with a higher signal level relative to the noise level and retain a greater signal to noise ratio.
Same cable, same run, line verses mic level signal- the common mode interference noise will be at the same level in both cases. But the line-level signal has a higher RMS voltage than the mic-level signal, so the difference between the noise level and signal level is greater with the line-level signal. When the mic-level signal is amplified to the same level as the line-level signal, the noise is also amplified by the same amount. So noise increases by the same amount as the level difference between the mic-level and line-level signals. Good balanced cables allow you to start with a lower noise level, but regardless of what that beginning noise level actually is, it is going to be amplified as much as the signal is amplified. Starting with a higher level signal means the noise needn't be amplified as much.
Unbalanced mic cables need to be kept short to avoid HF rolloffs for impedance reasons, and 10' is typically a good general limit there. I've run line-level unbalanced signals 40' without problems using two 20' RCA's plugged together for soundboard feeds. I was somewhat concerned about interference, but haven't had problems doing it. Again, a the strong line-level signal helps there.