At 60 degrees f, jumping from zero to 50% humidity will cost you roughly 1% in air density. You might like to think about it like this. For a given volume, the water molecules displace the air molecules.
Therefore from lift formula, CL 1/2 rho Vsquared S, you need a greater V or TAS as in this case. Greater TAS, higher groundspeed, more runway used to achieve the same IAS for takeoff.
Also ground run increases because less thrust or HP for props, produced by the engine, not taking into account flat rated engines below their rated temp. Hope this helps.
A very simplified answer, I await the boffins inevitable expansion.