Let us say I have an LED whose brightness or luminance value is 50 Cd/m2. If I lit 10 same type of LEDs with same conditions of current and voltage then will the brightness of these 10 LEDs will add up to 500 Cd/m2 or will it give some other value?
It depends if the radiated light is diffused over the same area.
50Cd/m^2 = 50 nits would be a dim desktop monitor or a bright mobile.
Adding 10 in the same area with diffusion makes that 10x brighter.
But if not diffused each source would not appear to be brighter by neighbouring LEDs but the flux of radiated light would brighten the reflected light by 10x. The same is true with Xmas lights.
You're comparing apples and oranges when you refer to 'brightness' and 'luminance'.
'Brightness' is 'how bright is the light when I look at it', while 'luminance' is 'how will lit is the surface the light is shining on'.
Luminance is additive - if you shine more lights on the same surface, the surface gets more light.
Brightness is not additive - putting a light next to another light doesn't make either of them brighter.
Yes, luminance is additive, 10 LEDs illuminating a given surface gives you 10 times more cd/m² than a single LED.