one short and one long speaker cable work?

If they're worth anything, no, keep the cable length the same.

But in terms of electrical theory, it's hard to imagine a 14 ga or larger speaker cable sounding very different at 6 or 2 meters. 

Yes you can use RJ45 cable extenders: 
I was afraid they'll introduce noise and hence reduce speed in our LAN but finally there was no perceptible difference.

Yes, you are fine.  The only thing unequal length cable affects may be resale value.

Rich

I was always told to keep speaker cable length equal or as close to equal between sides as possible, as impedance difference would become an issue. Though, that may have changed.
Bob

I was referring to each pair of speaker wire. Having them significantly unmatched in length is supposed to be a no no.
B

I would never do that.....same length for me....both interconnects and speaker wire.

Then it would be out of phase. And, you know how my delicate ears hate that.
B

I think Geoff is saying the sound between the two cables will be inperceivable. A typical speaker cable with low impedance will not have an audible difference between such short lengths. 

Keep your cables as is and dont coil them.

You could always go to a local hardware store and pick up 8M of wire and cut it into a 2M and 6M lengths and try to hear a difference between your AQ's at equal length. Listen for imaging and soundstage not the differences in tonality.

Cables should always be the same size.

How about two different brands of the same length, conductor metal and gauge? Is that a no no?

@geoffkait .
I don't think it would damage anything, but knowing that different brands have different sound qualities, why bother?
The question the OP posed was whether it wise to use unequal lengths.
Where's Almarg when we need him?
B

Why bother? Because the shortfall of one brand might be made up by the other brand. E.g., frequency response. And visa versa. It’s the same idea why sometimes two different brands of cables are run in parallel to each speaker.

Different cables? ..even with the same manufacturer  - Yuk

It is not like you are building cables and deciding what lengths to purchase.  You already own a pair of 19-feet long cables so just leave both sides at the same length.  Cutting them will ruin the resale potential.  If possible, run the short side around somewhere inconspicuous without coiling it up.  You can always try coiling or not and determine whether you hear a difference.

You could always purchase and terminate bulk cable in the lengths you need.  Try the linked cable.  For your 10M needs, you will need two rolls of 25 feet, which would give you about 15M total.  The cable is 10 gauge,  99.997% OFHC C10100 Copper in foamed polyethylene insulation (FPE) - all for $21 per 25 feet!  Check out the economical pure copper (plated or unplated) Furez connectors (also from  from the same vendor).  You could be all-in at the lengths you need for less than $100.  
https://www.avoutlet.com/cables-connectors/bulk-cables/speaker/in-wall-cl3/furez-fz102as-25/

Thanks to all who have offered their expertise and experience on this issue; I appreciate your advise.