I have a line in my noise texture when I render it, it's really visible. I'm using Cycles, with a spherified, subdivided, cube. I also let it smart UV unwrap, but the gap was still there. blend file
You need to include a Displacement node.
Use the color mask you've generated as the Height input.
When you connect the color without conversion, it generates this line.
If we switch from Bump Only to Displacement and Bump we can see why.
(Note that I have only connected the Noise Texture to the Material Output in this image. With the MixRGB node the effect is even more pronounced.)
Both the noise texture output and the color being Added are grayscale values, and when you attach a color directly to the Displacement input it treats it as Vector Displacement. This means it translates the entire mesh some amount on all axes. With the way I had my camera rotated it's going up left.
When Blender represents this type of mesh deformation in Bump Only, it is this sphere with a smooth line across the center where all the motion is "up left" and it's difficult to see the bumpiness.
Perhaps better put: if you consider that new diagonal the axis you're operating upon, those pixels at the "equator", as it were, aren't operated upon in a way that can be represented without actually moving them.