Does it matter if the shunt resister in an audio Line Out L-Pad attenuator is 6 feet away from the series resister?
Does the placement of the shunt at the other end of the 6 foot cable
change the tone or have any other detrimental impact?

No, I don't believe this will be a problem.
6 foot (say 2 metres) will have a capacitance of around 200 to 300 pF so, worst case low pass roll-off will occur at: -
$$f = \dfrac{1}{2\pi R C}\hspace{1cm} = \text{ 24 kHz}$$
But this assumes the 5k6 resistor is open circuit so, in reality it will be circa 100 kHz and not an issue for audio.