Filling in Bounded Region Mathematica Graph

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I am trying to shade the regions bound by a function and a horizontal and vertical line. The region bounded region under the graph where n2[g]>0.3 where g<2^(1/3) to be green and the area where n2[g]>0.3 where g>2^(1/3) to be red. I have code for an image that does this, but the shaded region also appears to be above the graph. How do I get rid of these circled shaded regions?

The functions and code are attached below. I used a conditional shading function found on a different thread (https://mathematica.stackexchange.com/questions/37468/conditional-options-in-plot)

graph of function and shaded regions

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