The average total energy as well as its hadronic and electromagnetic components are measured with the CMS detector at pseudorapidities $-$6.6 $<$ $\eta$ $<-$5.2 in proton-proton collisions at a centre-of-mass energy $\sqrt{s} =$ 13 TeV. The results are presented as a function of the charged particle multiplicity in the region $|\eta|$ $<$ 2. This measurement is sensitive to correlations induced by the underlying event structure over a very wide pseudorapidity region. The predictions of Monte Carlo event generators commonly used in collider experiments and ultra-high energy cosmic ray physics are compared to the data. All generators considered overestimate the fraction of energy going into hadrons.