设函数$f\left(x\right)=x^3+x,x\in R$. 若当$0<\theta <\frac{\mathrm{\pi }}{2}$时，不等式$f\left(m\sin \theta \right)+f\left(1-m\right)>0$恒成立，则实数m的取值范围是（   ）.

Dear Diary,

    What a day!I started at my new school this morning and had a great time.I made lots of new friends and really liked my teachers.I was so nervous last night,but I had no reason(原因) to be .Everyone was so friendly.They made me feel at home!

    The day started very early at 7：00am.I had breakfast with my mum.She could tell(看出)that I was very anxious.Mum kept asking me what was wrong. I thought she knew that I was nervous about starting at a new school. She told me I had nothing to worry about and that everyone would be friendly and love me.

    My mum dropped me off(让我下车)at the school gate at about 7：50 am．A little girl with fair hair got dropped off at the same time and started waving at me．She ran over and told me her name was Abigail．It turned out that we were in the same class．Abigail was very nice and we became close right away．We spent all morning together and began to talk with another girl called Stacey．The three of us sat together in class all day and we even made our way home together! Time went by so quickly．Our teacher told us that tomorrow we would really start learning and developing new skills(技能)．

    It is late now so I am going to sleep,but I cannot wait till tomorrow!I believe I'm going to enjoy my time at my new school!I hope that my new friends feel the same too．

Casey

根据材料内容选择最佳答案。

若不等式x﹣$\frac{3}{2}$＜2x﹣$\frac{5}{2}$+1的最小整数解是方程2x﹣ax=4的解，求a的值．