What wire do I need to power 10m of SK9822 LED strip
Look closely at the PCB traces on the LED strips and ask yourself "can I realistically expect this to carry 36A?" 

Mind you, Electrical Code says a 36A load is too big even for 10AWG wire.   Go to a home improvement store and handle some 10AWG wire for yourself.  See what I mean? It's pretty big stuff. 

Much worse, even though your distance isn't far, voltage drop is rather ouchey when you're starting with only 12V. So run your numbers through a voltage drop calculator just to make sure you're not dropping too much.  

Feeder everywhere

Look at any trolley-bus system in Dayton, San Francisco, Philly, Vancouver, Toronto, Boston, or any former Eastern Bloc country.  You can do it on Google Earth, Hayes St. in San Francisco is a good example.    They have two #2/0 trolley wires feeding the bus.  But up on the electric poles is also a pair of Very Fat Wires, and every 3-4 poles a fat jumper wire from a trolley wire to one of the fat wires.  They are almost 2" diameter and solid aluminum.  They are feeder.  The 2/0 trolley wires simply can't carry enough current to supply a whole line full of trolley buses, so the feeder takes most of the line's current. Any bus is supplied via the trolley wire from both directions down to the nearest jumper to the feeder.

So you do the same thing.  You won't have more than 30A in either direction, so 10AWG feeder will probably suffice.  You run positive and negative (traditional colors red and black) parallel to the strips the entire length.  And you tie it to the LED strips proper everywhere you possibly can, such as all those breaks that you need anyway.  

You could even feed each strip from both ends if you want to, in which case the feeder is paralleled to the internal bus in the strips.  That is fine, like the trolleybus, because it is DC.  Do not parallel AC wires.