\((7x-11^3)=5^2\cdot2^5+5^2\cdot2^3\)
\(\Rightarrow(7x-11^3)=5^2\cdot(2^5+2^3)\)
\(\Rightarrow(7x-11^3)=25\cdot(32+8)\)
\(\Rightarrow(7x-11^3)=25\cdot40\)
\(\Rightarrow(7x-11^3)=1000\)
\(\Rightarrow7x=1000+11^3\)
\(\Rightarrow7x=1000+1331\)
\(\Rightarrow7x=2331\)
\(\Rightarrow x=333\)