Property $R_\infty$ for Artin and Coxeter groups whose outer automorphisms are length-preserving

We prove that every length-preserving automorphism of a nonspherical Artin or Coxeter group has infinite Reidemeister number. As a consequence, we establish property $R_\infty$ for large-type free-of-infinity Artin groups, infinite strongly rigid Coxeter groups, and infinite virtually abelian Coxete