How to do addition of sound pressure RMS in a DFT
The power spectrum of the DFT is the square of the magnitudes and is related to the power spectrum of the discrete time signal by Parsevel's theorem:

$$E_x=\sum_{k=0}^{N-1}\lvert x[k]\rvert ^2=\frac{1}{N}\sum_{k}^{N-1}\lvert X[k]\rvert^2.$$

The RMS is just the square root of the power. (I assume you've already taken care of the 1/N since you mentioned your DFT is already in the correct units).

$$\textrm{RMS}_{x}=\sqrt{\sum_{k=0}^{N-1}\lvert X[k]\rvert^2}.$$

You can compute the RMS of a range of bins $[i,j]$ by constraining $k$.

$$\textrm{RMS}_{x_{ij}}=\sqrt{\sum_{k=i}^{j}\lvert X[k]\rvert^2}.$$