##C, 112 101 96 98 bytes
Thanks to @MartinEnder for saving 5 3 bytes while fixing my code!
j,i,k,l;f(char*s){l=strlen(s);for(i=l;j<l;)k+=(s[j++]-48)*(i>1?i--:-1);return!(k%11)&&k&&(l^8)<2;}
Returns 0 if invalid, 1 if valid. Try it online!