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Inelastic neutron scattering is used to measure spin excitations in fully deuterated single crystal samples of the strong-leg antiferromagnetic S=1/2 spin ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_4$. Sharp resolution-limited magnons are observed acr oss the entire one-dimensional Brillouin zone. The results validate the previously proposed {it symmetric} spin ladder model and provide a reliable estimate of the relevant exchange interactions.
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