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How to increase height of square brackets in legend label?

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I'd like the square brackets to be taller in the following legend label, so that they extend as high as the 6 in $10^6$. The most success I've had is by using MaTeX, but I'd prefer a built-in solution, because MaTeX looks really inconsistent with all the other text in the image.

Note that LabelStyle -> 10 makes the output look worse than it would otherwise, because the "6" superscript seems to look extra large compared to the way it looks normally. So a partial solution would just be to shrink the size of the exponent somehow. But still, I'd prefer to keep the exponent as is and just increase the height of the brackets.

LineLegend[{Red, Green, Blue}, {1, 2, 3},  LegendLabel -> "d [\!\(\*SuperscriptBox[\(10\), \(6\)]\) km]",  LabelStyle -> 10]

enter image description here


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