$\frac{x+1}{15}$ +$\frac{x+2}{14}$ =$\frac{x+5}{11}$ +$\frac{x+4}{12}$
⇔$\frac{14.(x+1)+15(x+2)}{210}$ =$\frac{12(x+5)+11(x+4)}{132}$
⇔$\frac{14x+14+15x+30}{210}$ =$\frac{12x+60+11x+44}{132}$
⇔$\frac{29x+44}{210}$ =$\frac{23x+104}{132}$
⇔132 (29x+44) = 210 (23x+104)
⇔3828x+5808 = 4830x+21840
⇔3828x-4830x=21840-5808
⇔-1002x=16032
⇔x=-16