Exposure value changes but image brightness remains same (Nikon D5600, Manual Mode)

I don't know that Nikon, but usually in manual mode the exposure meter is "display only", showing the exposure you get with the current parameters.

For the exposure to actually be an input, you would need to be on one of the "less manual" settings, where the camera is responsible for computing some of the values. For canons that would be Av/Tv, where you set the aperture and the camera finds the exposition time to achieve that exposure; or you set the exposition time and the camera sets the aperture.

the +/- button on the top of the camera, by the shutter button, changes the aperture when in manual mode. If you haven't changed the iso off of auto, the iso will change when you change when you change the aperture.

This is in fact expected. Manual mode changes the exposure by adjusting exposure parameters: Shutter-Speed, Aperture and ISO.

Exposure-Compensation is for adjusting an automatically metered exposure, so has no effect in manual mode. The meter you see is actually an indication of how far off the camera considers the set exposure compared to the metered one. When you adjust EC (+/-) you are adding a bias from to the metered exposure so that what is shown is the difference between the metered exposure +/- the dialed-in EC compared to the manually chosen exposure.