If $3x-10=-(2x+5)$, then the numerical value of $(x-4{)}^3$ is:

First, let's solve the linear equation for $x$:
$$3x-10=-2x-5$$
$$3x+2x=-5+10$$
$$5x=5⟹x=1$$
Now, substitute $x=1$ into the given expression $(x-4{)}^3$:
$$(1-4{)}^3=(-3{)}^3=-27$$