SINAD is just 1kHz tone (at a certain specified level) in relation to all 'crap' levels that should not be there converted to dB and the dB naming and sign removed.
You cannot simply 'add' dBs in this case. They represent level differences.
You need to convert dB's to linear levels, add the levels and then convert back to dB.
110 is 3x higher in level than 120.
100 is 10x higher in level than 120
80 is 100x higher in level than 120
We have to add levels. The levels are very, very, very small and below any audible threshold levels.
Even SINAD 80 (depending on the harmonic spread) is probably only audible in lab conditions with extremely good speakers/headphones, trained listening to pure tones.
When you add very, very, small amounts of levels to 100x higher levels this is not going to be audible nor really visible in numbers and impossible to hear as the relatively massive amounts of 'unwanted crap) are 'masking (overwhelming)' the minute added crap.
With music, being dynamic in nature and signals masking other signals you really cannot detect crap that is even louder than the music unless it is constant in level (say noise, hum, or other constant noises). Distortion levels, however, go up and down determined by the actual levels and harmonics in the music will mask those tiny, tiny levels anyway.
For this reason it matters if we are looking at distortion while considering music. It is not the same as test tones as all kinds of perception aspects is going on.