Brilleslyper and Schaubroeck's unit-circle root-count conjecture for trinomials

Let $n,m\in\mathbb N$ satisfy

$$\gcd(n,m)=1.$$

Consider the trinomial $x^n+x^m-1$, and let the interior of the unit circle mean $\{z\in\mathbb C:|z|<1\}$.

Brilleslyper and Schaubroeck's conjecture. The number of roots of $x^n+x^m-1$ in the interior of the unit circle is

$$2\left\lfloor\frac{n+m-1}{6}\right\rfloor+1.$$

The formula extends the proved special case $m=1$, for which the source gives the count $2\lfloor n/6\rfloor+1$. The coprime general case is stated as a conjecture and is open in the supplied text.