Concentrated wormlike micellar fluids form the basis for a vast array of formulated products, from liquid soaps and shampoos to drag reduction and drilling fluids. Typically, these systems are analyzed using bulk rheological measurements to determine their flow properties and cryo-microscopy to detect their nanostructure. Smallangle neutron scattering provides an opportunity to directly and nonperturbatively analyze nanostructure in situ but is complicated for concentrated systems by correlations from interparticle volume exclusion. Here, we use small-angle and ultra-small-angle neutron scattering to probe directly for the first time the nanostructure of concentrated wormlike micellar fluids composed of the widely used surfactant pair sodium laureth sulfate and cocamidopropyl betaine in aqueous electrolytes. Obtained data are analyzed using different approaches to determine scattering contributions from the wormlike particles themselves and interactions between them. It is found that approximating worms as locally rigid cylinders offers some insight into their aggregation dimensions at short length scales, and both volume exclusion and screened Coulombic interaction potentials describe interactions reasonably well. Using the semi-empirical polymer reference interaction site model (PRISM) gives excellent agreement with observed scattering, and physical insight obtained using this approach is discussed in detail. A drawback of this method is the significant complexity in coding the model in order to fit data, so to facilitate this for future researchers, we provide with this paper a fully operational, open-source code to utilize this model.