When you uncoil the cable it will be laying flat on the ground with no twists.
An alternative for massive cables it lay it out in a figure 8 on the ground. That will also pay out without twists.
Extension: The upright vacuum cleaner you've been using that releases the cord from the handle by twisting the top hook down? If it is leaving you with a twisted mess of cord, that means you haven't been winding it up in a figure 8.
Even more, since you got this far: Do this with your short cables too. Your USB and audio cables will last longer. When you have a twisted cable, a torque shows up at each individual wire where it meets its connector. The repeated twisting and untwisting leads to connection failure.
And when you get a new cable that is rolled up (any Apple cable), unroll it instead of pulling the ends apart. Then you cable need never have twists put into it.